Rate of Thermal Conduction

In Chapter 3 we presented model equations for heat exchangers with our mixed–mixed, mixed–plug, and plug–plug classifications. All these fluid motions generally require some degree of turbulence, and all heat exchangers, except for those for which there is direct contact between phases, require a solid surface dividing the two control volumes of the exchanger. To predict the overall heat transfer coefficient, denoted as U in the analyses in Part I, we must be able to determine how U is affected by the turbulent eddies in the fluids and the physical properties of the fluids and how the rate of heat transfer depends on the conduction of heat through the solid surface of the exchanger.

We begin our study of conductive transport by considering the transfer of heat in a uniform solid such as that employed as the boundary between the two control volumes of any exchanger. This requires a Level III analysis and verification of a constitutive equation for conduction. This is followed by a complementary analysis of molecular diffusion through solids and stagnant fluids.

Experimental Determination of Thermal Conductivity k and Verification of Fourier's Constitutive Equation

Consider an experiment whereby the heat flow through the wall between the tank and the jacket in Figure 3.7 is measured. For the purposes of this analysis, we consider the heat transfer to be essentially one dimensional in the y direction, with the barrier essentially infinite in the z–x plane.